A Sunderland fan in the North Stand appeared to perform the gesture after Lukaku had scored in the 4-2 win at the Stadium of Light.
Police are now looking into the incident surrounding the Belgian international, who is on a season-long loan from Chelsea.
A Sunderland spokesman said: "SAFC operates a policy of zero tolerance towards racism and antisocial behaviour of any kind.
"Naturally we will co-operate with the police in fully investigating any such incidents."
The incident comes in the wake of alleged anti-Semitic chanting by West Ham supporters during Sunday's defeat at Tottenham.
"There should be no place in the game, or in any walk of life, for some of the things that have transpired within stadiums over the weekend," said Baggies' boss Steve Clarke.
"The authorities are now looking into the incident at Sunderland and Romelu has our full support.
"I am sure the authorities will conduct a thorough inquiry and take the appropriate action."